1) constructing assistant function
构造辅助函数
1.
By using the method of Lagrange constant coefficient transformation,combining with the solution of boundary value problem of dif-ferential coefficient,this paper introduces a new solution for constructing assistant function.
利用 Lagrange 常数变易法，结合常微分方程中的边值问题的解法，给出了构造辅助函数的一种新方法。
3) auxiliary function
辅助函数
1.
Parameter alternating method to construct the auxiliary function;
利用参数变导法构造辅助函数
2.
Several ways of establishing auxiliary function to testi fy median proposition;
中值命题证明中构造辅助函数的几种方法
3.
On the construction of auxiliary function when using the calculous intermediate value theorem;
谈微分中值定理运用中辅助函数的构建
4) supplementary function
辅助函数
1.
A supplementary function can be given.
通过给出关于凹凸函数的一个性质定理及其推论,对一些特定类型的三角不等式通过构造辅助函数,求出函数的二阶导数;再结合其凹凸性利用定理的推论给予简捷的证明。
2.
This paper, by means of Rolle theorem, introduces constant method to demonstrate mean value theorem for differential calculus and attains the corresponding supplementary function of the demonstrating method.
借助于Rolle定理,用待定常数法证明了微分中值定理,得到了该证明方法的辅助函数簇,这种证明方法对解决同类问题有很好的推广应用价值。
3.
In this paper,a new structural method of supplementary function is introduced, and the method is used to prove differential identical equation or integral inequality.
本文给出辅助函数新的构造方法 ,并将它运用于微分恒等式和积分不等式的证
5) auxiliary functions
辅助函数
1.
By constructing auxiliary functions and ordinary differential equations, we have obtained some new exact traveling wave solutions of the nonlinear coupled KdV equations which include soliton wave solutions and periodic solutions.
利用构造辅助函数和辅助常微分方程组的方法,给出了非线性耦合KdV方程的某些新的精确行波解,其中包括孤波解和周期解。
2.
By constructing auxiliary functions,some new exact traveling wave solutions of the nonlinear coupled VB equations are obtained,which include solitary wave solutions,trigonometric function solutions,Jacobian elliptic function solutions and rational solutions,and some solutions are complex linear solutions.
利用构造辅助函数的方法,给出了非线性耦合VB方程组的某些新的精确行波解,包括孤子解、三角函数解、椭圆函数解和幂函数解,其中某些解还是复线型的。
3.
By constructing auxiliary functions, we have obtained some new exact traveling wave solutions of the nonlinear coupled KdV equations which include solitary wave solutions, trigonometric function solutions,Jacobian elliptic function solutions and rational solutions.
利用构造辅助函数的方法,给出了非线性耦合KdV方程的某些新的精确行波解,其中包括孤子解,三角函数解,椭圆函数解和幂函数解。
6) assistant function
辅助函数
1.
Constructing assistant functions in Proofing the Mean-Value Theorem;
中值定理证明中辅助函数的构造
2.
For example,when teaching the construction of Assistant Function in Differential Mean-value Theorem,we can introduce them the idea of inversion thought;when teaching the Series,we can lead them to establish the relation between Series and Limit by use of inversion thought.
结合高等数学中部分典型知识点,介绍在平时教学中如何培养和训练学生的逆向思维能力,如在讲授微分中值定理时,通过辅助函数的构造向学生介绍逆推法;在级数的教学中,引导学生利用逆推法建立级数和极限间的关系。
3.
How to cultivate students creative thinking during the process of proving the Lagrange Value Theorem is briefly described,this can be achieved with the help of imagination and guess,and should be based on the combination of the condition and conclusion of the theorem,as well as the construction of the assistant function.
结合拉格朗日中值定理的教学,简述了定理证明过程中如何利用想象和猜想,联系定理的条件和结论构造定理的辅助函数,对学生进行创造性思维的培养。
补充资料：构造函数论
构造函数论
constructive theory of functions
构造函数论【~如出ve the哪of俪川姗;~TPy-盯恤妞a，Teop“，中挤K明““〕 由c.H.BepHllrl‘H弓!人的一个概念，他称构造函数论为“函数论的一个分支，旨在对自然提出的数学分析问题的解函数和经验函数的定量研究和计算提供最简单、最方便的基础”([l}).应当指出，构造函数论包括函数逼近论作为它的一个分支.但是，当实际使用“构造函数论一词时，则取较狭窄的意义.就是指函数逼近论，现在已很少使用“构造函数论”词t补注1 {A 11 Ibr吧movl 1 On Bernsteins contrlbut;onst。，the mnstrlJ改jve万heoryo生，1、川成一005 In(一i川exlts and 5 B.Stechk，n(eds飞.Proc.C‘、nf.Constrtl以IveT址- ory ofl、J们Ctl‘，r，s、Akad.幻n啪.1969，27一40(俄_文)_ !AZ]sze乡，〔1.、I决、contributions、，fl一Fej打tot吮con- str一Ictivef助说lon theory.In(，Alex一ts and 5 B. Steellk，n(ed熟，，Proc(’onf(onstructive Jheo:y of F朋以ions，Ak之肤iK一nd6.1969 19一26
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